In electrically heated glass melting furnaces with multiple electrode levels, it is known to connect the electrodes of the uppermost level in such a manner that their current paths meet in the center of the furnace (U.S. Pat. No. 3,852,509). However, with this circuit arrangement, it has been found that the concentration of energy within the center of the furnace becomes excessive in the uppermost plane, and that an insufficient amount of energy is supplied to the furnace periphery. Cold spots can result between electrodes, particularly in the corners of hexagonal furnace walls. In such cold spots, the not yet molten glass batch or unrefined molten glass might descend to the furnace bottom. Furthermore, control is difficult to maintain with this circuit arrangement because the power inputs for the various levels of electrodes are matched to each other so as to be controllable simultaneously and in the same sense only.